Answer:
x = 3 ± √6.
or 0.55, 5.45 to the nearest hundredth.
Step-by-step explanation:
(x−3)^2+2=8
(x - 3)^2 = 8 - 2 = 6
(x - 3)^2 = 6
Taking square roots of both sides:
x - 3 = +/- √6
x = 3 ± √6.
ㅤ
Given quadratic equation:-
⇢ [tex]\rm{(x - 3) 2 + 2 = 8}[/tex]
ㅤ
Simplifying the given equation:-
ㅤ
1) Simplify both sides of the equation.
⇢ [tex]\rm{x^{2} - 6x + 11 = 8}[/tex]
ㅤ
2) Subtract (8) from both sides, we get:
⇢ [tex]\rm{x^{2} - 6x + 11 - 8 = 8 - 8}[/tex]
⇢ [tex]\rm{x^{2} - 6x + 3 = 0}[/tex]
ㅤ
3) In the equation: (a = 1), (b = -6), (c = 3):
⇢ [tex]\rm{1x^{2} + - 6x + 3 = 0}[/tex]
ㅤ
4) Use quadratic formula:
⇢ [tex]\rm{x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}[/tex]
⇢ [tex]\rm{x = \dfrac{-(-6) \pm\sqrt{(-6)^{2} - 4 (1) (3)}}{2 \times 1}}[/tex]
⇢ [tex]\rm{x = \dfrac{6 \pm \sqrt{4}}{2}}[/tex]
